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Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments
(2021)
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation–maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.
Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein–protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01–0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625–0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.
New drugs are urgently needed to combat the global TB epidemic. Targeting simultaneously multiple respiratory enzyme complexes of Mycobacterium tuberculosis is regarded as one of the most effective treatment options to shorten drug administration regimes, and reduce the opportunity for the emergence of drug resistance. During infection and proliferation, the cytochrome bd oxidase plays a crucial role for mycobacterial pathophysiology by maintaining aerobic respiration at limited oxygen concentrations. Here, we present the cryo-EM structure of the cytochrome bd oxidase from M. tuberculosis at 2.5 Å. In conjunction with atomistic molecular dynamics (MD) simulation studies we discovered a previously unknown MK-9-binding site, as well as a unique disulfide bond within the Q-loop domain that defines an inactive conformation of the canonical quinol oxidation site in Actinobacteria. Our detailed insights into the long-sought atomic framework of the cytochrome bd oxidase from M. tuberculosis will form the basis for the design of highly specific drugs to act on this enzyme.
Photolabile protecting groups are widely used to trigger oligonucleotide activity. The ON/OFF‐amplitude is a critical parameter. An experimental setup has been developed to identify protecting group derivatives with superior caging properties. Bulky rests are attached to the cage moiety via Cu‐catalyzed azide–alkyne cycloaddition post‐synthetically on DNA. Interestingly, the decrease in melting temperature upon introducing o‐nitrobenzyl‐caged (NPBY‐) and diethylaminocoumarin‐cages (DEACM‐) in DNA duplexes reaches a limiting value. NMR spectroscopy was used to characterize individual base‐pair stabilities and determine experimental structures of a selected number of photocaged DNA molecules. The experimental structures agree well with structures predicted by MD simulations. Combined, the structural data indicate that once a sterically demanding group is added to generate a tri‐substituted carbon, the sterically less demanding cage moiety points towards the neighboring nucleoside and the bulkier substituents remain in the major groove.
The ATP-binding cassette transporter TAPL translocates polypeptides from the cytosol into the lysosomal lumen. TAPL can be divided into two functional units: coreTAPL, active in ATP-dependent peptide translocation, and the N-terminal membrane spanning domain, TMD0, responsible for cellular localization and interaction with the lysosomal associated membrane proteins LAMP-1 and LAMP-2. Although the structure and function of ABC transporters were intensively analyzed in the past, the knowledge about accessory membrane embedded domains is limited. Therefore, we expressed the TMD0 of TAPL via a cell-free expression system and confirmed its correct folding by NMR and interaction studies. In cell as well as cell-free expressed TMD0 forms oligomers, which were assigned as dimers by PELDOR spectroscopy and static light scattering. By NMR spectroscopy of uniformly and selectively isotope labeled TMD0 we performed a complete backbone and partial side chain assignment. Accordingly, TMD0 has a four transmembrane helix topology with a short helical segment in a lysosomal loop. The topology of TMD0 was confirmed by paramagnetic relaxation enhancement with paramagnetic stearic acid as well as by nuclear Overhauser effects with c6-DHPC and cross-peaks with water.